We prove that every compact space $X$ is a Čech-Stone compactification of a normal subspace of cardinality at most $d(X)^{t(X)}$, and some facts about cardinal invariants of compact spaces.
@article{118679,
author = {Anatoly A. Gryzlov},
title = {Cardinal invariants and compactifications},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {35},
year = {1994},
pages = {403-408},
zbl = {0807.54005},
mrnumber = {1286587},
language = {en},
url = {http://dml.mathdoc.fr/item/118679}
}
Gryzlov, Anatoly A. Cardinal invariants and compactifications. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 403-408. http://gdmltest.u-ga.fr/item/118679/
Vpolne zamknutye otobrazhenija, Matem. sbornik 99:1 (1976), 3-33. (1976)
Stroenie i klassifikacija topologicheskich prostranstv i kardinalnye invarianty, Uspekhi mat. nauk 33:6 (1978), 29-84. (1978) | MR 0526012
O teoreme E. Čecha, Vest. MGU 6 (1979), 54-57. (1979) | MR 0561409
On cardinal invariants of compact spaces, Abstr. Baku Intern. Top. Conf., 1987, p. 89.
O vlozhenii ekstremalno-normalnyh prostranstv v bikompakty, Dokl. Akad. Nauk SSSR 223:5 (1975), 1083-1086. (1975) | MR 0394609
O nasledstvenno normalnykh prostranstvah, Abstr. VII Vses. Top. Conf. Minsk, 1977, p. 204.
O moschnosti bikompaktov s pervoi aksiomoi schetnosti, Dokl. Akad. Nauk SSSR 187 (1969), 967-970. (1969) | MR 0251695